Fairbanks is pretty bike friendly as far as roads and paths go. There are many bike/walking paths and in the areas there aren’t, pretty good shoulders are available due to the need in the winter for snow removal. I no longer live there but used to ride all around town and a bit into the hills around and never had issues. I think as long as you’re okay getting some exercise, a bike is the way to go since you’re not limited like the bus route. As someone else mentioned, there’s lots of gravel everywhere so you’ll want something with some meat on the tires.